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  2. Pivotal quantity - Wikipedia

    en.wikipedia.org/wiki/Pivotal_quantity

    Then is called a pivotal quantity (or simply a pivot). Pivotal quantities are commonly used for normalization to allow data from different data sets to be compared. It is relatively easy to construct pivots for location and scale parameters: for the former we form differences so that location cancels, for the latter ratios so that scale cancels.

  3. Ancillary statistic - Wikipedia

    en.wikipedia.org/wiki/Ancillary_statistic

    A ancillary statistic is a specific case of a pivotal quantity that is computed only from the data and not from the parameters. They can be used to construct prediction intervals. They are also used in connection with Basu's theorem to prove independence between statistics. [4]

  4. Fiducial inference - Wikipedia

    en.wikipedia.org/wiki/Fiducial_inference

    The pivotal method is based on a random variable that is a function of both the observations and the parameters but whose distribution does not depend on the parameter. Such random variables are called pivotal quantities. By using these, probability statements about the observations and parameters may be made in which the probabilities do not ...

  5. Prediction interval - Wikipedia

    en.wikipedia.org/wiki/Prediction_interval

    Such a pivotal quantity, depending only on observables, is called an ancillary statistic. [2] The usual method of constructing pivotal quantities is to take the difference of two variables that depend on location, so that location cancels out, and then take the ratio of two variables that depend on scale, so that scale cancels out.

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  7. Nuisance parameter - Wikipedia

    en.wikipedia.org/wiki/Nuisance_parameter

    In some special cases, it is possible to formulate methods that circumvent the presences of nuisance parameters. The t-test provides a practically useful test because the test statistic does not depend on the unknown variance but only the sample variance. It is a case where use can be made of a pivotal quantity. However, in other cases no such ...

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    The recommendation for anyone taking a tirzepatide and an oral birth control pill is to use a backup barrier method like a condom for the first four weeks and then for four weeks after each dose ...

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